Employers posted 4.64 million jobs, a 3.8 percent increase from April’s total of 4.46 million, the Labor Department said Tuesday. That was the fourth straight strong gain and the highest number since June 2007.

The figures follow last week’s healthy jobs report and underscore this year’s steady improvement in hiring. Employers added a net total of 288,000 jobs in June, the government said last week, the fifth straight month of gains above 200,000. That was the first such stretch in 15 years. The unemployment rate fell to a five-year low of 6.1 percent.

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Tuesday’s report, known as the Job Openings and Labor Turnover survey, offered a more complete picture of the job market. It reported figures for overall hiring, as well as the number of resignations and layoffs. The monthly jobs figures are a net total of job gains or losses.

Some details of Tuesday’s report were not as encouraging.

Employers have been slow to fill
jobs, which suggests they are having trouble finding workers with the right skills.

Total hiring actually slipped in May, to 4.72 million from 4.77 million in April. But the number of people quitting jobs rose 60,000 to 2.5 million, the highest level since June 2008.

The chairwoman of the Federal Reserve, Janet Yellen, has said she is tracking the overall hiring and quitting figures as indicators of the job market’s health and dynamism.

Both quitting and hiring remain below their prerecession levels, evidence that the job market is not yet back to full health.

In the past year, job openings have increased nearly 20 percent. But total hiring has risen just 4 percent.

Some economists say that is a sign many of those out of work don’t have the skills needed for the jobs available. Former construction workers and factory employees, for example, may not be able to fill new jobs in health care or other growing fields.

Others argue that companies will have to offer higher pay to attract the workers they need. That could boost overall wages, which have barely kept up with inflation since the recession ended five years ago.

There are other signs pay could rise soon. There are now 2.1 unemployed workers, on average, for every job opening. That is the ratio that typically exists in a healthy economy and indicates employers may have to try harder to fill jobs, perhaps by boosting salaries.

‘‘We think the result is going to be a pickup in wage growth,’’ said Cooper Howes, US economist at Barclays Capital.

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